Radha Kessar

The principal block of a Z_p-spets

Do there exist structures associated to finite complex reflection groups that play the same role as finite reductive or compact Lie groups play for finite Weyl groups? The Broué-Malle-Michel theory of spetses associates to certain complex reflection groups combinatorially defined data sets with properties consistent with Lusztig's unipotent character theory for finite reductive groups. On the other hand, the Dwyer-Wilkerson theory of p-compact groups associates to p-adic (complex) reflection groups topological spaces which possess much of the structure of compact groups. In this talk, I will show how combining spetsial theory with the theory of p-compact groups can be used to define the notion of the principal p-block of a spets which on a numerical level looks very much like the block of a finite group. This is joint work with Gunter Malle and Jason Semeraro.